Well, set up your favorite form of an equation of a line. It should probably have an x, a y, and two or three more variables (parameters) in it. The fact that the line passes through (2,-3) should give you an equation and/or some other fact about the parameters. The fact that the line is tangent to that parabola should give you more information.

Alternatively, find the tangent line to the parabola at a general point, and see which of those lines pass through (2,-3).

Hi guys
can you please help me with the following question
I really don't how to start with this question
Thanks

Here comes a slightly different approach to this problem:

1. A line passing through (2, -3) has the equation:

3. Calculate the coordinates of the points of intersection of the parabola and the line:

Solve for x:

3. A line is tangent to the parabola if there exist only one point of intersection: the tangent point. This is only possible if the dicriminant equals zero:

Plug in these values into the equation of the line at 2.

4. The x-coordinate of the tangent point is . Plug in the values of m to get the x-coordinates and plug in the x-coordinates into the equation of the line to get the corresponding y-coordinates of the tangent points.

5. For confirmation draw a sketch of the parabola and the two lines. (My sketch isn't drawn to scale!)